1. A common activity is to give children pattern blocks, Tangrams, or other tiles to construct shapes. Identify the van Hiele level of geometric thought emphasized in these types of activities. Why are these types of activities valuable for children? (Chapter 20)
The van Hiele level of geometric thought, when children use any types of tiles to make shapes, is level-0 because it is part of the visualization process. Children should be given time to play with these tiles so they can use their imagination to create as many shapes as they can. Not to mention that the teacher can choose a level of difficulty for the students so that it can be challenging. Activities like these ones are valuable because when children make figures out of shapes, they are paying attention to the use of a variety of shapes that can be seen around them; in their homes, schools, parks, and more. The book mentions (on page 407) how beneficial it is to have the students draw their own figures onto paper. This can help by allowing students to clearly see the shapes they used. Most importantly, teachers can start a discussion with questions about the corners, vertices, lines/sides, convex, concave, etc. The children will even be able to learn a lot better because they are experimenting with it first-hand.
2. Technology makes it very easy to compute statistics and create graphs of all types. What is the value of using technology for these puposes? (Chapter 21)
In my opinion, when using technology to graph statistical information, children should be guided through a fun and interesting activity in order for them to understand what a graph is used for. How they can sort all type of information and in many different ways. On pages 443 and 449, the book has little sections that explain how beneficial technology can be for students. For example, the variety of ways to graph like in a graphing calculator or software on a computer that offers all sorts of graphs for specific uses. There are even some programs that graph in 3D! This makes it more fun for children because they see their illustration, or function, come to life. By capturing their attention in this way, they pay more attention to the information they gathered and will analyze the differences and/or similarities.
3. Describe the difference between experimental probability and theoretical probability. Will these ever be the same? Which is the "correct" probability? (Chapter 22)
Experimental probability is when you test out, or experiment, something and you count the number of times it occurred over the amount of times you tried it. Theoretical probability counts the amount of outcomes over the amount of outcomes that were possible. I do not think that they will be the same because theoretical probabilty only takes into account the number of outcomes that are possible,or were completed. Whereas, experimental probability takes more trials and counts all of them at the end. It is like it works as a science experiment and runs a number of tests until you have reached positive outcomes. I feel that the "correct" probability is experimental, because you are searching the positive outcomes of something in comparison to the trials that failed. So, when using experimental probability you do not count the total of outcomes that were a "maybe" or were possible.
Review Questions #5
1. A common activity is to give children pattern blocks, Tangrams, or other tiles to construct shapes. Identify the van Hiele level of geometric thought emphasized in these types of activities. Why are these types of activities valuable for children? (Chapter 20)
The van Hiele level of geometric thought, when children use any types of tiles to make shapes, is level-0 because it is part of the visualization process. Children should be given time to play with these tiles so they can use their imagination to create as many shapes as they can. Not to mention that the teacher can choose a level of difficulty for the students so that it can be challenging. Activities like these ones are valuable because when children make figures out of shapes, they are paying attention to the use of a variety of shapes that can be seen around them; in their homes, schools, parks, and more. The book mentions (on page 407) how beneficial it is to have the students draw their own figures onto paper. This can help by allowing students to clearly see the shapes they used. Most importantly, teachers can start a discussion with questions about the corners, vertices, lines/sides, convex, concave, etc. The children will even be able to learn a lot better because they are experimenting with it first-hand.
2. Technology makes it very easy to compute statistics and create graphs of all types. What is the value of using technology for these puposes? (Chapter 21)
In my opinion, when using technology to graph statistical information, children should be guided through a fun and interesting activity in order for them to understand what a graph is used for. How they can sort all type of information and in many different ways. On pages 443 and 449, the book has little sections that explain how beneficial technology can be for students. For example, the variety of ways to graph like in a graphing calculator or software on a computer that offers all sorts of graphs for specific uses. There are even some programs that graph in 3D! This makes it more fun for children because they see their illustration, or function, come to life. By capturing their attention in this way, they pay more attention to the information they gathered and will analyze the differences and/or similarities.
3. Describe the difference between experimental probability and theoretical probability. Will these ever be the same? Which is the "correct" probability? (Chapter 22)
Experimental probability is when you test out, or experiment, something and you count the number of times it occurred over the amount of times you tried it. Theoretical probability counts the amount of outcomes over the amount of outcomes that were possible. I do not think that they will be the same because theoretical probabilty only takes into account the number of outcomes that are possible,or were completed. Whereas, experimental probability takes more trials and counts all of them at the end. It is like it works as a science experiment and runs a number of tests until you have reached positive outcomes. I feel that the "correct" probability is experimental, because you are searching the positive outcomes of something in comparison to the trials that failed. So, when using experimental probability you do not count the total of outcomes that were a "maybe" or were possible.